TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/CURRENT-RESPONSE-AND-DICTIONARY.md
Original file SHA-256: db9163de1017810818e104f651e531247378a4c8295580c8936cb19e594b4b73
Inclusive original lines: 10-92
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000010 | 
000011 | Use the original `_actual_current_source` Chevalley currents and compact
000012 | adjoint, not an abstract matrix algebra chosen to fit the answer. Its
000013 | twenty currents X_ia carry bar(5) tensor 4; F_ia=X_ia^dagger carry
000014 | 5 tensor bar(4). The four original charged currents C_a carry 1 tensor 4.
000015 | These are weight-one currents, not established physical fermion fields.
000016 | 
000017 | Set B_ia,jb=[X_ia,F_jb], C_ij=(sum_a B_ia,ja)/4,
000018 | T=sum_i C_ii, S_ij=C_ij-delta_ij T/5 and Z=-4T/9. Actual brackets give
000019 | T|F=-9/4, T|C=-15/4 and hence Z|F=1, Z|C=5/3.
000020 | For a five-by-five matrix H define the actual source current
000021 | 
000022 |     Q(H)=-sum_ij (H-tr(H)I/5)_ij S_ji + tr(H)Z/5.
000023 | 
000024 | Then
000025 | 
000026 |     [Q(H),F_ka]=sum_j H_jk F_ja,
000027 |     [Q(H),C_a]=tr(H) C_a/3,
000028 |     kappa(Q(H),Q(K))=tr(HK)-tr(H)tr(K)/9.
000029 | 
000030 | `check_current_response.py` checks all 500 matrix-unit/field actions and
000031 | 625 current-form matrix-unit pairs exactly in the original source.
000032 | Noncommuting H on the unresolved E+ plane therefore have an actual
000033 | noncommuting source action. This reuses the existing E8 Ward algebra;
000034 | the new result is its comparison with the actual native code/clock map.
000035 | 
000036 | For the existing polar direction c and projector P, put
000037 | 
000038 |     h_R=cc* + P tau/2.
000039 | 
000040 | Its eigenvalues are 1, +1/2, -1/2, 0, 0; exp(i pi h_R)=R5.
000041 | The source zero-mode exponential exp(i pi Q(h_R)_0) is an inner
000042 | automorphism, preserving the stipulated vacuum and conformal vector.
000043 | The source form is kappa(Q(h_R),Q(h_R))=25/18, identically for the WHOLE
000044 | previous CP1 marking fibre. Neither this norm nor existence of the
000045 | exponential selects the original polar point, pulse strength or time.
000046 | 
000047 | There is a concrete separated-point distinction. For Y=(5P-2I)/6,
000048 | the actual Ward responses <Q(Y)(-1) F(0) X(1)> have kinematic factor -1/2.
000049 | Using the original normalized source ray q and even-plane vector e1:
000050 | 
000051 | | Mark | q,q response | q,e1 response |
000052 | |---|---:|---:|
000053 | | Original polar mark | 0 | -sqrt(6)/12 |
000054 | | Previously defined countermark c=e0 | 1/6 | 0 |
000055 | 
000056 | Thus the source can distinguish these specified marks. A distinguishable
000057 | amplitude does not supply a law choosing one mark or a physical detector.
000058 | 
000059 | ## 2. A genuine full-source order-four lift exists
000060 | 
000061 | Requiring R5 on F leaves three finite inner source automorphisms in this
000062 | gl5 family. Since det R5=-1, logarithms H of R5 have
000063 | tr H=pi(2k+1). Their action on C is scalar c=exp(i pi(2k+1)/3):
000064 | 
000065 | | tr(H)/pi modulo 6 | c | Order on full source |
000066 | |---|---|---:|
000067 | | 1 | exp(i pi/3) | 12 |
000068 | | 3 | -1 | 4 |
000069 | | 5 | exp(-i pi/3) | 12 |
000070 | 
000071 | The C and F currents with adjoints generate the stipulated E8 source,
000072 | so their joint action fixes the full automorphism. The order-four branch
000073 | is obtained, for example, using h_R+2cc*. Different logarithms with the
000074 | same finite endpoint do not select a unique continuous generator.
000075 | It would be incorrect to claim an unavoidable period-twelve obstruction.
000076 | 
000077 | ## 3. What matches at the finite native group, and what does not
000078 | 
000079 | The checker compares ALL 60 original event charts with the actual
000080 | quartic code action using Gaussian-integer compression. The comparison
000081 | uses the original oriented determinant-path lift h=lambda r,
000082 | lambda=exp(-i pi/4). Its source five-action is
000083 | 
000084 |     A5=lambda^4 rho5(r)=-rho5(r).
000085 | 
000086 | The opposite currents F then transform as
000087 | 
000088 |     A5 tensor bar(h)=lambda^3 rho5(r) tensor bar(r).
000089 | 
000090 | This is exactly the actual W20 intertwiner action of h^tensor3. Its
000091 | central square is +i. It is a statement about the coupled finite cover
000092 | <G31,zeta8 I> intersect SU4, not the unchanged order-two word r in G31.